Implications of long tails in the distribution of mutant effects

Long-tailed distributions possess an in nite variance, yet a nite sample that is drawn from such a distribution has a nite variance. In this work we consider a model of a population subject to mutation, selection and drift. We investigate the implications of a long-tailed distribution of mutant allelic e¤ects on the distribution of genotypic e¤ects in a model with a continuum of allelic e¤ects. While the analysis is confined to asexual populations, it does also have implications for sexual populations. We obtain analytical results for a selectively neutral population as well as one subject to selection. We supplement these analytical results with numerical simulations, to take into account genetic drift. We nd that a long-tailed distribution of mutant e¤ects may a¤ect both the equilibrium and the evolutionary adaptive behaviour of a population

The homestake surface-underground scintillations: Description

Two new detectors are currently under construction at the Homestake Gold Mine a 140-ton Large Area Scintillation Detector (LASD) with an upper surface area of 130 square meters, a geometry factor (for an isotropic flux) of 1200 square meters, sr, and a depth of 4200 m.w.e.; and a surface air shower array consisting of 100 scintillator elements, each 3 square meters, spanning an area of approximately square kilometers. Underground, half of the LASD is currently running and collecting muon data; on the surface, the first section of the air shower array will begin operation in the spring of 1985. The detectors and their capabilities are described

Apparent Superluminal Behavior

The apparent superluminal propagation of electromagnetic signals seen in recent experiments is shown to be the result of simple and robust properties of relativistic field equations. Although the wave front of a signal passing through a classically forbidden region can never move faster than light, an attenuated replica of the signal is reproduced ``instantaneously'' on the other side of the barrier. The reconstructed signal, causally connected to the forerunner rather than the bulk of the input signal, appears to move through the barrier faster than light.Comment: 8 pages, no figure

(3+2) Neutrino Scheme From A Singular Double See-Saw Mechanism

We obtain a 3+2 neutrino spectrum within a left-right symmetric framework by invoking a singular double see-saw mechanism. Higgs doublets are employed to break $SU_{R}(2)$ and three additional fermions, singlets under the left-right symmetric gauge group, are included. The introduction of a singularity into the singlet fermion Majorana mass matrix results in a light neutrino sector of three neutrinos containing predominantly $\nu_{\alpha L}$, $\alpha=e,\mu,\tau$, separated from two neutrinos containing a small $\nu_{\alpha L}$ component. The resulting active-sterile mixing in the $5\times 5$ mixing matrix is specified once the mass eigenvalues and the $3\times3$ submatrix corresponding to the MNS mixing matrix are known.Comment: 5 pages, matches published versio

Born's rule from measurements of classical signals by threshold detectors which are properly calibrated

The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement scheme which transforms continuous signals into discrete clicks and reproduces the Born's rule. This is the sheme of threshold type detection. Calibration of detectors plays a crucial role.Comment: The problem of double clicks is resolved; hence, one can proceed in purely wave framework, i.e., the wave-partcile duality has been resolved in favor of the wave picture of prequantum realit

Energy Levels of "Hydrogen Atom" in Discrete Time Dynamics

We analyze dynamical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. In particular we study the problem of discrete energy levels of hydrogen atom. We are able to reconstruct potential which in discrete time formalism leads to energy levels of unperturbed hydrogen atom. We also consider linear energy levels of quantum harmonic oscillator and show how they are produced in the discrete time formalism. More generally, we show that in discrete time formalism finite motion in central potential leads to discrete energy spectrum, the property which is common for quantum mechanical theory. Thus deterministic (but discrete time!) dynamics is compatible with discrete energy levels.Comment: accepted for publication in Open Systems & Information Dynamic

Evolutionary trajectories in rugged fitness landscapes

We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the most populated genotype \textit{jumps} from a local fitness maximum to another and eventually reaches the global maximum. We use a strong selection limit, which reduces the dynamics beyond the first time step to the competition between independent mutant subpopulations, to study the dynamics of this model and of a simpler one-dimensional model which ignores the geometry of the sequence space. We find that the fit genotypes that appear along a trajectory are a subset of suitably defined fitness \textit{records}, and exploit several results from the record theory for non-identically distributed random variables. The genotypes that contribute to the trajectory are those records that are not \textit{bypassed} by superior records arising further away from the initial population. Several conjectures concerning the statistics of bypassing are extracted from numerical simulations. In particular, for the one-dimensional model, we propose a simple relation between the bypassing probability and the dynamic exponent which describes the scaling of the typical evolution time with genome size. The latter can be determined exactly in terms of the extremal properties of the fitness distribution.Comment: Figures in color; minor revisions in tex

A Natural Framework for Solar and 17 keV Neutrinos

Motivated by recent experimental claims for the existence of a 17 keV neutrino and by the solar neutrino problem, we construct a class of models which contain in their low-energy spectrum a single light sterile neutrino and one or more Nambu-Goldstone bosons. In these models the required pattern of breaking of lepton-number symmetry takes place near the electroweak scale and all mass heirarchies are technically natural. The models are compatible with all cosmological and astrophysical constraints, and can solve the solar neutrino problem via either the MSW effect or vacuum oscillations. The deficit in atmospheric muon neutrinos seen in the Kamiokande and IMB detectors can also be explained in these models.Comment: 23 page

Gamow-Teller Strengths for Neutrino Detectors

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Adaptive walks on time-dependent fitness landscapes

The idea of adaptive walks on fitness landscapes as a means of studying evolutionary processes on large time scales is extended to fitness landscapes that are slowly changing over time. The influence of ruggedness and of the amount of static fitness contributions are investigated for model landscapes derived from Kauffman's $NK$ landscapes. Depending on the amount of static fitness contributions in the landscape, the evolutionary dynamics can be divided into a percolating and a non-percolating phase. In the percolating phase, the walker performs a random walk over the regions of the landscape with high fitness.Comment: 7 pages, 6 eps-figures, RevTeX, submitted to Phys. Rev.